Statistical Modelling 7 (2007), 175–190
A measure of partial association for generalized estimating equations
Sundar Natarajan
Department of Medicine,
New York University School of Medicine,
and the VA New York Harbor Healthcare System,
423 East 23rd Street, Room 15160-North
New York, NY 10010-5013
USA
eMail:
sundar.natarajan@med.nyu.edu
Stuart Lipsitz
Division of General Internal Medicine,
Brigham and Women's Hospital
USA
Michael Parzen
Goizueta Business School,
Emory University
USA
Stephen Lipshultz
Department of Pediatrics,
University of Miami School of Medicine
USA
Abstract:
In a regression setting, the partial correlation coefficient is often
used as a measure of ‘standardized’ partial association
between the outcome y and each of the covariates in
x' = [x1, . . . , xK].
In a linear regression model estimated using ordinary
least squares, with y as the response, the estimated partial
correlation coefficient between y and xk can be
shown to be a monotone function, denoted f (z), of
the Z–statistic for testing if the regression
coefficient of xk is 0. When y is
non–normal and the data are clustered so that y
and x are obtained from each member of a
cluster, generalized estimating equations are
often used to estimate the regression parameters of
the model for y given x. In this paper, when using
generalized estimating equations, we propose using the
above transformation f (z) of the
GEE Z–statistic as a measure of partial
association. Further, we also propose a coefficient
of determination to measure the strength of
association between the outcome variable and all
of the covariates. To illustrate the method, we use a
longitudinal study of the binary outcome heart
toxicity from chemotherapy in children with leukaemia
or sarcoma.
Keywords:
coefficient of determination; longitudinal data; repeated measures
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